The research is rooted in performance-based earthquake engineering, a framework that treats structures not as objects that simply stand or fall, but as systems whose performance can be predicted probabilistically. At the heart of this framework sits the intensity measure, a scalar descriptor of ground shaking, such as peak ground acceleration or spectral acceleration at a given period, that serves as the bridge between hazard analysis and structural response prediction. The quality of an intensity measure is judged by its efficiency, meaning how tightly it correlates with the engineering demand parameters that describe structural and operational damage, and by its sufficiency, meaning how well the predicted response remains independent of other ground-motion characteristics. An intensity measure that is both efficient and sufficient allows engineers to build accurate probabilistic seismic demand models with fewer costly simulations, which is precisely where the new study makes its contribution.

The particular system the researchers examined, known as the simply-supported-bridge-vehicle coupled system, is among the most common bridge forms on high-speed railway networks, especially on challenging routes such as the Sichuan-Tibet Railway, where lines must cross regions laced with active strike-slip faults. Simply supported spans rest on bearings that allow rotation and, to a degree, translation, which makes them economical and constructible but also vulnerable when the ground beneath them lurches in two directions at once. When a train is present, the problem becomes even more intricate, because the vehicle, the track, and the bridge form a dynamically coupled system in which the running safety of the train depends on the deformation of the deck, and the vibration of the deck is in turn influenced by the moving masses of the vehicles above it. Past investigations by these and other research groups have shown that near-fault pulse-type ground motions can compromise derailment resistance and that fault rupture itself imposes permanent, quasi-static displacements that no amount of dynamic damping can absorb.

Strike-slip faulting introduces a uniquely punishing combination of effects. As the fault ruptures, the ground on either side shears horizontally past the other, and a structure crossing the fault trace is forced to accommodate the offset. In the near-fault zone, two signature phenomena dominate: the fling step, a permanent, often unidirectional displacement pulse produced by tectonic deformation, and forward directivity, a strong long-period velocity pulse that arrives when the rupture front propagates toward the site at nearly the speed of the shaking itself. These effects are inherently directional, aligned with the fault-parallel and fault-normal orientations, so the structural response depends critically on the angle at which the bridge crosses the fault. Compounding the challenge, recorded ground motions close to strike-slip surface ruptures are scarce, forcing analysts to work with limited datasets in which the choice of intensity measure carries outsized consequences for the reliability of the resulting risk estimates.

To tackle this problem, the team developed a modified intensity measure selection framework for cloud analysis, a widely used statistical technique in which a family of ground motion records, each scaled or unscaled, is run through the structural model and the resulting demands are regressed against candidate intensity measures in logarithmic space. The innovation lies in the normalization of the intensity measures, which sharpens the comparison of efficiency across candidates whose raw numerical ranges differ by orders of magnitude. By normalizing before evaluating statistical performance, the framework reduces distortions that can arise in regression diagnostics and produces a fairer ranking of alternatives. The researchers then applied the framework across a battery of candidate measures drawn from the standard toolbox of earthquake engineering, including peak ground velocity, peak spectral displacement, peak spectral velocity, and measures defined from individual ground motion components as well as geometric-mean combinations, testing each against six representative engineering demand parameters spanning the bridge and the running vehicles.

The verdict from thousands of coupled dynamic analyses is strikingly clear: under the coupled fling-step and forward-directivity demands of crossing strike-slip faulting, velocity- and displacement-based spectral measures outperform the acceleration-based measures that have traditionally dominated fragility studies. Specifically, the peak spectral displacement, SDmax, and peak spectral velocity, SVmax, emerged as the top performers for constructing probabilistic seismic demand models of the coupled system. This makes physical sense. Long-period velocity pulses and permanent displacement offsets, the hallmarks of near-fault strike-slip motion, resonate most directly with displacement-type demands such as bearing displacement, pier drift, and the deck deformations that govern train running safety. Peak ground acceleration, by contrast, emphasizes high-frequency content that is relatively less consequential for these long-period, quasi-static-dominated failure modes, and its correlation with demand weakens accordingly.

Equally important is the finding about directionality. The study shows that intensity measures computed from the fault-parallel component of ground motion perform consistently well in integrated assessments across all six engineering demand parameters, reflecting the dominant role of the shearing displacement imposed along the fault trace. When the researchers turned to specific engineering scenarios defined by the fault-bridge crossing angle, they identified scenario-specific optima: for a 90-degree crossing, the geometric mean of peak spectral displacement across the two horizontal components, SDmax,GM, proved best, while for a shallower 45-degree crossing, the fault-parallel peak spectral displacement, SDmax,FP, took the top spot. In both cases the chosen measures delivered a balanced combination of efficiency and sufficiency, giving engineers a defensible, defensible-to-auditor basis for record selection and fragility construction tailored to the actual geometry of a proposed crossing.

The practical implications reach well beyond academic statistics. High-speed rail corridors in tectonically active regions, from southwest China to Turkey, California, and Taiwan, increasingly must traverse fault zones because alternative routings are economically or geographically impossible. The 1999 Kocaeli and Duzce earthquakes in Turkey and the Chi-Chi earthquake in Taiwan famously collapsed or displaced simply supported spans whose unseated girders traced the fault rupture across their alignments. By identifying which ground-motion descriptors most faithfully capture the demand imposed on a coupled bridge-train system, the new framework enables more economical and more trustworthy fragility assessment, supporting decisions about bearing seat widths, restrainers, isolation systems, and operational speed limits during seismic events. Because cloud analysis with unscaled records is computationally expensive, the improved efficiency of the recommended measures also translates directly into fewer simulations required for a given confidence level, a meaningful saving when each coupled vehicle-track-bridge analysis involves extensive nonlinear computation.

Methodologically, the study also contributes a reusable template. The normalization-based cloud analysis framework is not tied to any particular bridge form, and the authors’ evaluation metrics, which weigh efficiency, sufficiency, and practicality across multiple demand parameters simultaneously, can be redeployed for continuous girders, cable-stayed spans, and suspension bridges crossing faults, where prior work by the same community has documented severe track-bridge interaction and long-span dynamic amplification. The research was supported by the National Natural Science Foundation of China, the Department of Education of Guangdong Province, the Foshan Science and Technology Bureau, and Hunan University of Science and Technology, and drew on the strong-motion database of the Pacific Earthquake Engineering Research Center’s Next Generation Attenuation-West2 project. As high-speed rail networks push deeper into seismically hostile mountains and basins, the humble task of choosing the right number to describe a ground motion, once treated as a technical footnote, now stands revealed as one of the decisive levers for keeping trains, bridges, and passengers safe when the ground itself refuses to hold still.

Subject of Research: Selection of optimal seismic intensity measures for railway simply-supported-bridge-vehicle coupled systems subjected to crossing strike-slip faulting.

Article Title: Analysis and selection of seismic intensity measures for railway simply-supported-bridge–vehicle coupled systems subjected to crossing-strike-slip faulting

Article References: Zhou, T., Li, Z., Jiang, L., & Wen, T. (2026). Analysis and selection of seismic intensity measures for railway simply-supported-bridge–vehicle coupled systems subjected to crossing-strike-slip faulting. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02676-6

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02676-6

Keywords: seismic intensity measures, railway bridge, strike-slip fault, vehicle-bridge interaction, probabilistic seismic demand, fling step, forward directivity, cloud analysis, running safety, high-speed railway, fault crossing, earthquake engineering